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Finding all the circuits of a directed graph with self-arcs and multiple-arcs
-----------------------------------------------------------------------------
Algorithm and code by K.A. Hawick and H.A. James
Enumerating Circuits and Loops in Graphs with Self-Arcs and Multiple-Arcs
K.A. Hawick and H.A. James
Computer Science, Institute for Information and Mathematical Sciences,
Massey University, North Shore 102-904, Auckland, New Zealand
k.a.hawick@massey.ac.nz; heath.james@sapac.edu.au
Tel: +64 9 414 0800
Fax: +64 9 441 8181
Technical Report CSTN-013
Usage
-----
make
./circuits_hawick 4 0,1 0,2 1,0 1,3 2,0 3,0 3,1 3,2
First argument is the number of vertices. Subsequent arguments are ordered
pairs of comma separated vertices that make up the directed edges of the
graph.
DOT file input
--------------
For simplicity, there is no DOT file parser included but the following allows
to create a suitable argument string for simple DOT graphs.
Given a DOT file of a simple (no labels, colors, styles, only pairs of
vertices...) directed graph, the following line produces commandline
arguments in the above format for that graph.
echo `sed -n -e '/^\s*[0-9]\+;$/p' graph.dot | wc -l` `sed -n -e 's/^\s*\([0-9]\) -> \([0-9]\);$/\1,\2/p' graph.dot`
The above line works on DOT files like the following:
digraph G {
0;
1;
2;
0 -> 1;
0 -> 2;
1 -> 0;
2 -> 0;
2 -> 1;
}
It would produce the following output:
3 0,1 0,2 1,0 2,0 2,1
Reproducing the example from the paper
--------------------------------------
Figure 10 of the paper cited above:
0 10 11 6 13 3 4 15 0 1 8 4 13 12 1
0 10 11 6 13 12 1 8 0 1 8 4 13 12 1
0 10 11 6 13 12 1 8 4 15 0 3 3
0 10 11 6 13 12 1 8 0 3 4 13 3
0 10 11 6 13 12 1 8 4 15 0 3 6 13 3
0 10 11 6 13 15 0 6 13 12 10 11 6
0 14 11 6 13 3 4 15 0 6 13 12 14 11 6
0 14 11 6 13 12 1 8 0 8 8
0 14 11 6 13 12 1 8 4 15 0 9 9
0 14 11 6 13 12 1 8 0 12 12
0 14 11 6 13 12 1 8 4 15 0
0 14 11 6 13 15 0
Figure 10: 22 Circuits found in the network shown in figure 9 which has 16
nodes and 32 arcs and allows self-arcs. Note there are repeated circuits due to
the presence of a multiple-arc connecting nodes 12 and 1.
The input graph, which is shown in figure 9, can be given as an input to the
program using above format as follows:
./circuits_hawick 16 0,2 0,10 0,14 1,5 1,8 2,7 2,9 3,3 3,4 3,6 4,5 4,13 \
4,15 6,13 8,0 8,4 8,8 9,9 10,7 10,11 11,6 12,1 12,1 12,2 12,10 12,12 \
12,14 13,3 13,12 13,15 14,11 15,0